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M
M
Hinges
M
M
M
p
Behaviour
0
0
(a ) Pl a s tic h i n g e s
(b) Frictionless hinge
Figure 5.27
Plastic hinge behaviour.
The infinite curvature at the point of full plasticity and the finite slope change
θ
predictedbytherigid-plasticassumptionleadtotheplastichingeconceptillus-
trated in Figure 5.27a.The plastic hinge can assume any slope change
θ
once the
full plastic moment
M
p
has been reached. This behaviour is contrasted with that
showninFigure5.27bforafrictionlesshinge,whichcanassumeanyslopechange
θ
at zero moment.
Itshouldbenotedthatwhenthefullplasticmoment
M
p
ofthesimplysupported
beam shown in Figure 5.26a is reached, the rigid-plastic assumption predicts that
a two-bar mechanism will be formed by the plastic hinge and the two frictionless
support hinges, as shown in Figure 5.25b, and that the beam will deform freely
without any further increase in load, as shown in Figure 5.26c. Thus the ultimate
load of the beam is
Q
ult
=
4
M
p
/
L
,
(5.34)
which reduces the beam to a plastic collapse mechanism.
5.5.3 Moment redistribution in indeterminate beams
The increase in the full plastic moment
M
p
of a beam over its nominal first yield
moment
M
y
is accounted for in elastic design (i.e. design based on an elastic
analysis of the bending of the beam) by the use of
M
p
for the moment capacity
of the cross-section. Thus elastic design might be considered to be 'first hinge'
design. However, the feature of plastic design which distinguishes it from elastic
design is that it takes into account the favourable redistribution of the bending
momentwhichtakesplaceinanindeterminatestructureafterthefirsthingeforms.
This redistribution may be considerable, and the final load at which the collapse
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